Restrictive Stochastic Item Selection Methods in Cognitive Diagnostic Computerized Adaptive Testing

This paper proposes two new item selection methods for cognitive diagnostic computerized adaptive testing: the restrictive progressive method and the restrictive threshold method. They are built upon the posterior weighted Kullback‐Leibler (KL) information index but include additional stochastic components either in the item selection index or in the item selection procedure. Simulation studies show that both methods are successful at simultaneously suppressing overexposed items and increasing the usage of underexposed items. Compared to item selection based upon (1) pure KL information and (2) the Sympson‐Hetter method, the two new methods strike a better balance between item exposure control and measurement accuracy. The two new methods are also compared with Barrada et al.'s (2008) progressive method and proportional method.     

认知诊断自适应测试的应用与展望

基于认知诊断自适应测试(CD-CAT)的教育测量技术能够为学生个性化学习提供帮助,有助于做到因材施教。目前我国已开展基于CD-CAT教育辅助系统的开发和使用,但与其他国家和地区相比较仍有差距。扩大教育测量专业人员队伍,加强CD-CAT在理论上的创新研究、在实践上的应用,开发更加适合个人、更加开放灵活的智能学习系统是我国教育测量的未来发展方向。     

2PLM下CAT选题策略比较

本文在两参数逻辑斯蒂克模型（2PLM）下,提出一种新的选题策略——平均测验难度匹配法（Avt—b）,并对四种选题策略下EAP能力估计趋势进行比较研究。通过模拟研究显示,Avt—b方法在CAT前期能够较快地锁定能力范围,较准确地作出能力估计。本文对CAT测试阶段的能力误差范围进行确定,对于多级评分模型的CAT选题策略开发具有一定的借鉴意义。     

An Efficiency Balanced Information Criterion for Item Selection in Computerized Adaptive Testing

Successful administration of computerized adaptive testing (CAT) programs in educational settings requires that test security and item exposure control issues be taken seriously. Developing an item selection algorithm that strikes the right balance between test precision and level of item pool utilization is the key to successful implementation and long‐term quality control of CAT. This study proposed a new item selection method using the “efficiency balanced information” criterion to address issues with the maximum Fisher information method and stratification methods. According to the simulation results, the new efficiency balanced information method had desirable advantages over the other studied item selection methods in terms of improving the optimality of CAT assembly and utilizing items with low a‐values while eliminating the need for item pool stratification.     

On the Issue of Item Selection in Computerized Adaptive Testing With Response Times

Many standardized tests are now administered via computer rather than paper‐and‐pencil format. The computer‐based delivery mode brings with it certain advantages. One advantage is the ability to adapt the difficulty level of the test to the ability level of the test taker in what has been termed computerized adaptive testing (CAT). A second advantage is the ability to record not only the test taker's response to each item (i.e., question), but also the amount of time the test taker spends considering and answering each item. Combining these two advantages, various methods were explored for utilizing response time data in selecting appropriate items for an individual test taker. Four strategies for incorporating response time data were evaluated, and the precision of the final test‐taker score was assessed by comparing it to a benchmark value that did not take response time information into account. While differences in measurement precision and testing times were expected, results showed that the strategies did not differ much with respect to measurement precision but that there were differences with regard to the total testing time.     

Multistage Computerized Adaptive Testing With Uniform Item Exposure

This article describes a computerized adaptive test (CAT) based on the uniform item exposure multi-form structure (uMFS). The uMFS is a specialization of the multi-form structure (MFS) idea described by Armstrong, Jones, Berliner, and Pashley (1998 Armstrong, R. D., Jones, D. H., Berliner, N. and Pashley, P. June 1998. Computerized adaptive tests with multiple form structures, June, Champaign-Urbana, IL: Paper presented at the annual meeting of the Psychometric Society.  [Google Scholar]). In an MFS CAT, the examinee first responds to a small fixed block of items. The items comprising that block may be unrelated to each other, or they may comprise a testlet (Wainer and Kiely, 1987 Wainer, H. and Kiely, G. L. 1987. Item clusters and computerized adaptive testing: A case for testlets. Journal of Educational Measurement, 24: 185–201. [Crossref], [Web of Science ®] , [Google Scholar]) After the first block of items has been administered, adaptation takes place in the choice of the next block to be administered and subsequent blocks. The uMFS design integrates item exposure control, as well as content balancing and other test development needs, into the design of the CAT, instead of placing those activities in the online implementation. We show that it is possible to implement item exposure control, in a very thorough way, in the psychometric specifications of the item blocks.     

Item Selection in Computerized Adaptive Testing: Should More Discriminating Items be Used First?

During computerized adaptive testing (CAT), items are selected continuously according to the test-taker's estimated ability. The traditional method of attaining the highest efficiency in ability estimation is to select items of maximum Fisher information at the currently estimated ability. Test security has become a problem because high-discrimination items are more likely to be selected and become overexposed. So, there seems to be a tradeoff between high efficiency in ability estimations and balanced usage of items. This series of four studies with simulated data addressed the dilemma by focusing on the notion of whether more or less discriminating items should be used first in CAT. The first study demonstrated that the common maximum information method with Sympson and Hetter (1985) control resulted in the use of more discriminating items first. The remaining studies showed that using items in the reverse order (i.e., less discriminating items first), as described in Chang and Ying's (1999) stratified method had potential advantages: (a) a more balanced item usage and (b) a relatively stable resultant item pool structure with easy and inexpensive management. This stratified method may have ability-estimation efficiency better than or close to that of other methods, particularly for operational item pools when retired items cannot be totally replenished with similar highly discriminating items. It is argued that the judicious selection of items, as in the stratified method, is a more active control of item exposure, which can successfully even out the usage of all items.     

Item Selection and Exposure Control Methods for Computerized Adaptive Testing with Multidimensional Ranking Items

The use of computerized adaptive testing algorithms for ranking items (e.g., college preferences, career choices) involves two major challenges: unacceptably high computation times (selecting from a large item pool with many dimensions) and biased results (enhanced preferences or intensified examinee responses because of repeated statements across items). To address these issues, we introduce subpool partition strategies for item selection and within-person statement exposure control procedures. Simulations showed that the multinomial method reduces computation time while maintaining measurement precision. Both the freeze and revised Sympson-Hetter online (RSHO) methods controlled the statement exposure rate; RSHO sacrificed some measurement precision but increased pool use. Furthermore, preventing a statement's repetition on consecutive items neither hindered the effectiveness of the freeze or RSHO method nor reduced measurement precision.     

Computerized Cognitive Diagnostic Adaptive Testing: Effect on Remedial Instruction as Empirical Validation

The purpose of this study is to show the usefulness of cognitive diagnoses for remedial instruction. Cognitive diagnoses were done by an adaptive testing system using the rule-space methodology, which was developed by K. K. Tatsuoka and her associates (K. K. Tatsuoka, 1983, 1990; K. K. Tatsuoka & M. M. atsuoka, 1987; M. M. Tatsuoka & K. K. Tatsuoka, 1989). The results of the study strongly indicate that knowing students'knowledge states prior to remediation is very effective and that the rule-space method can effectively diagnose students' knowledge states and can point out ways for remediating their errors quickly with minimum effort. It is also found that the design of instructional units for remediation can be effectively guided by the rule-space model, because the determination of all possible knowledge states in a domain of interest, given an incidence matrix, is based on a partially ordered tree structure of knowledge states, which is equivalent to item-score patterns determined logically from the incidence matrix.     

IRT在计算机自适应测验与认知诊断中的应用

项目反应理论(Item Response Theory,IRT)是在克服经典测验理论局限性的基础上发展起来的,在单维性、局部独立性和单调性的前提假设下,更具有优越性。它以潜在特质理论为基础,采用项目特征曲线假设对其进行建模,产生了三个最基本的模型:正态肩型曲线模型、拉希模型和逻辑斯蒂模型。指出了IRT在实际应用中取得实质性进展的两个方面:计算机自适应测验和认知诊断。     

A Comparison of Item Exposure Control Methods in Computerized Adaptive Testing

Two new methods for item exposure control were proposed. In the Progressive method, as the test progresses, the influence of a random component on item selection is reduced and the importance of item information is increasingly more prominent. In the Restricted Maximum Information method, no item is allowed to be exposed in more than a predetermined proportion of tests. Both methods were compared with six other item-selection methods (Maximum Information, One Parameter, McBride and Martin, Randomesque, Sympson and Hetter, and Random Item Selection) with regard to test precision and item exposure variables. Results showed that the Restricted method was useful to reduce maximum exposure rates and that the Progressive method reduced the number of unused items. Both did well regarding precision. Thus, a combined Progressive-Restricted method may be useful to control item exposure without a serious decrease in test precision.     

Effects of Practical Constraints on Item Selection Rules at the Early Stages of Computerized Adaptive Testing

The purpose of this study was to compare the effects of four item selection rules—(1) Fisher information (F), (2) Fisher information with a posterior distribution (FP), (3) Kullback-Leibler information with a posterior distribution (KP), and (4) completely randomized item selection (RN)—with respect to the precision of trait estimation and the extent of item usage at the early stages of computerized adaptive testing. The comparison of the four item selection rules was carried out under three conditions: (1) using only the item information function as the item selection criterion; (2) using both the item information function and content balancing; and (3) using the item information function, content balancing, and item exposure control. When test length was less than 10 items, FP and KP tended to outperform F at extreme trait levels in Condition 1. However, in more realistic settings, it could not be concluded that FP and KP outperformed F, especially when item exposure control was imposed. When test length was greater than 10 items, the three nonrandom item selection procedures performed similarly no matter what the condition was, while F had slightly higher item usage.     

Assessing the Utility of Item Response Models: Computerized Adaptive Testing

How has Item Response Theory helped solve problems in the development and use of computer-adaptive tests? Do we need to balance item content with computer-adaptive tests? Could we use IRT to evaluate unusual responses to computer-delivered tests?     

A Comparative Study of Item Exposure Control Methods in Computerized Adaptive Testing

This study compared the properties of five methods of item exposure control within the purview of estimating examinees' abilities in a computerized adaptive testing (CAT) context. Each exposure control algorithm was incorporated into the item selection procedure and the adaptive testing progressed based on the CAT design established for this study. The merits and shortcomings of these strategies were considered under different item pool sizes and different desired maximum exposure rates and were evaluated in light of the observed maximum exposure rates, the test overlap rates, and the conditional standard errors of measurement. Each method had its advantages and disadvantages, but no one possessed all of the desired characteristics. There was a clear and logical trade-off between item exposure control and measurement precision. The Stocking and Lewis conditional multinomial procedure and, to a slightly lesser extent, the Davey and Parshall method seemed to be the most promising considering all of the factors that this study addressed.     

Item Clusters and Computerized Adaptive Testing: A Case for Testlets

It is observed that many sorts of difficulties may preclude the uneventful construction of tests by a computerized algorithm, such as those currently in favor in Computerized Adaptive Testing (CAT). In this essay we discuss a number of these problems, as well as some possible avenues of solution. We conclude with the development of the "testlet," a bundle of items that can be arranged either hierarchically or linearly, thus maintaining the efficiency of an adaptive test while keeping the quality control of test construction that is possible currently only with careful expert scrutiny. Performance on the separate testlets is aggregated to yield ability estimates.     

The Relationship Between Item Exposure and Test Overlap in Computerized Adaptive Testing

The purpose of this article is to present an analytical derivation for the mathematical form of an average between-test overlap index as a function of the item exposure index, for fixed-length computerized adaptive tests (CATs). This algebraic relationship is used to investigate the simultaneous control of item exposure at both the item and test levels. The results indicate that, in fixed-length CATs, control of the average between-test overlap is achieved via the mean and variance of the item exposure rates of the items that constitute the CAT item pool. The mean of the item exposure rates is easily manipulated. Control over the variance of the item exposure rates can be achieved via the maximum item exposure rate (r_max). Therefore, item exposure control methods which implement a specification of r_max (e.g., Sympson & Hetter, 1985) provide the most direct control at both the item and test levels.     

A Comparison of Procedures for Content-Sensitive Item Selection in Computerized Adaptive Tests

This simulation study compared two procedures to enable an adaptive test to select items in correspondence with a content blueprint. Trait level estimates obtained from testlet-based and constrained adaptive tests administered to 10,000 simulated examinees under two trait distributions and three item pool sizes were compared to the trait level estimates obtained from traditional adaptive tests in terms of mean absolute error, bias, and information. Results indicate that using constrained adaptive testing requires an increase of 5% to 11% in test length over the traditional adaptive test to reach the same error level and, using testlets requires an increase of 43% to 104% in test length over the traditional adaptive test. Given these results, the use of constrained computerized adaptive testing is recommended for situations in which an adaptive test must adhere to particular content specifications.     

Comparing Methods of Assessing Differential Item Functioning in a Computerized Adaptive Testing Environment

Mantel-Haenszel and SIBTEST, which have known difficulty in detecting non-unidirectional differential item functioning (DIF), have been adapted with some success for computerized adaptive testing (CAT). This study adapts logistic regression (LR) and the item-response-theory-likelihood-ratio test (IRT-LRT), capable of detecting both unidirectional and non-unidirectional DIF, to the CAT environment in which pretest items are assumed to be seeded in CATs but not used for trait estimation. The proposed adaptation methods were evaluated with simulated data under different sample size ratios and impact conditions in terms of Type I error, power, and specificity in identifying the form of DIF. The adapted LR and IRT-LRT procedures are more powerful than the CAT version of SIBTEST for non-unidirectional DIF detection. The good Type I error control provided by IRT-LRT under extremely unequal sample sizes and large impact is encouraging. Implications of these and other findings are discussed.     

Stratified and Maximum Information Item Selection Procedures in Computer Adaptive Testing

In this study we evaluated and compared three item selection procedures: the maximum Fisher information procedure (F), the a-stratified multistage computer adaptive testing (CAT) (STR), and a refined stratification procedure that allows more items to be selected from the high a strata and fewer items from the low a strata (USTR), along with completely random item selection (RAN). The comparisons were with respect to error variances, reliability of ability estimates and item usage through CATs simulated under nine test conditions of various practical constraints and item selection space. The results showed that F had an apparent precision advantage over STR and USTR under unconstrained item selection, but with very poor item usage. USTR reduced error variances for STR under various conditions, with small compromises in item usage. Compared to F, USTR enhanced item usage while achieving comparable precision in ability estimates; it achieved a precision level similar to F with improved item usage when items were selected under exposure control and with limited item selection space. The results provide implications for choosing an appropriate item selection procedure in applied settings.     

Evaluating Comparability in Computerized Adaptive Testing: Issues, Criteria and an Example

When a computerized adaptive testing (CAT) version of a test co-exists with its paper-and-pencil (P&P) version, it is important for scores from the CAT version to be comparable to scores from its P&P version. The CAT version may require multiple item pools for test security reasons, and CAT scores based on alternate pools also need to be comparable to each other. In this paper, we review research literature on CAT comparability issues and synthesize issues specific to these two settings. A framework of criteria for evaluating comparability was developed that contains the following three categories of criteria: validity criterion, psychometric property/reliability criterion, and statistical assumption/test administration condition criterion. Methods for evaluating comparability under these criteria as well as various algorithms for improving comparability are described and discussed. Focusing on the psychometric property/reliability criterion, an example using an item pool of ACT Assessment Mathematics items is provided to demonstrate a process for developing comparable CAT versions and for evaluating comparability. This example illustrates how simulations can be used to improve comparability at the early stages of the development of a CAT. The effects of different specifications of practical constraints, such as content balancing and item exposure rate control, and the effects of using alternate item pools are examined. One interesting finding from this study is that a large part of incomparability may be due to the change from number-correct score-based scoring to IRT ability estimation-based scoring. In addition, changes in components of a CAT, such as exposure rate control, content balancing, test length, and item pool size were found to result in different levels of comparability in test scores.